5 ms·
1. Alice, Bob and Charlie want to share a Cake so that none of them envies other pieces 2. Charlie cuts the cake into three pieces that are equally valuable fr
by tuco86 8y ago
1. Alice, Bob and Charlie want to share a Cake so that none of them envies other pieces
2. Charlie cuts the cake into three pieces that are equally valuable from his perspective
3. Alice identifies her first choice.
4. Bob identifies his first choice from the remaining two. Charlie gets the remaining one.
5. Bob trims either his or Alices piece.
6. Alice identifies her first choice.
Simpler. Is there a fault i don't see?
- QML 8y agoNow generalize to the case where the number of people = n.
- tuco86 8y agoI'm no mathematician. I just figured this whould work with 4 or 5 people by always removing one and extrapolated that it works for n. One devides and gets the worst based on the others opinions, then leaves with his piece. repeat.
- sp332 8y agoThe problem is if after step 5, Charlie thinks one of the new pieces is really good, and "envies" it.
- sk5t 8y agoIt's not a problem because Charlie starts by creating three slices of equal-to-Charlie value, and is guaranteed to receive one of those unmolested. If the other two participants value the pieces in some strange way, Charlie has no right to interfere.
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- kgwgk 8y ago[edit: not good, see next paragraph] Charlie did cut the pie in the first place, and he thought all the three pieces were equally good so he has to accept that he got a fair share. It's irrelevant that he finds that Alice and Bob didn't share fairly the rest of the cake. Edit: come on, are we really expected to read TFA or even to read carefully the first comment in the thread where it was clearly written “so that none of them envies other pieces” before commenting? (Seriously: I was obviously wrong. As punishment I leave my original comment here and now I’ll read the article five times.)
- sp332 8y agoAn allocation is envy-free if no agent would prefer to take another agent's allocation instead of his own. The problem they solved is much more difficult than the one you are describing.
- orthoxerox 8y agoIt's very relevant. Suppose the cake has 3 butter roses, and Charlie LOVES them. He cuts the cake into 3 pieces each with a rose on it, to get one in any case. Alice picks one piece, Bob picks another, Charlie gets the third. Now Bob thinks his piece is a bit too small compared to Alice's and transfers Alice's butter rose onto his piece. Alice either swaps or doesn't. Charlie now sees that either Alice or Bob has a cake piece with TWO butter roses and is VERY envious.
- tuco86 8y agoHe sees alice or bob with two butter roses on top of a smaller piece. Charlie has the first cut, so he can cut horizontally and make a tiny piece with 3 butter roses on top. he either gets his three butter roses or a bigger piece of cake, their relative value is still the same for him.
- klipt 8y ago> Is there a fault i don't see? What if Alice thinks that the piece Bob gave to Charlie was the 2nd best piece, and after Bob's trimming, the remaining pieces are both worse than what Charlie has?
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- CamperBob2 8y agoWhy do you need to go past step 5? Knowing that he will go last, Charlie has an incentive to cut the cake as evenly as possible. If he isn't happy with the result, he has no one but himself to blame. He can optimize his own share only by giving everyone the same amount.
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